single observation, but only that part of the motion that is in theline of sight. For a complete knowledge of a star's motion the propermotion and parallax must also be known.

When Huggins first applied the Doppler principle to measure velocitiesin the line of sight,[7] the faintness of star spectra diminished theaccuracy; but Vogel, in 1888, overcame this to a great extent by longexposures of photographic plates.

It has often been noticed that stars which seem to belong to a groupof nearly uniform magnitude have the same proper motion. Thespectroscope has shown that these have also often the same velocity inthe line of sight. Thus in the Great Bear, beta, gamma, delta,epsilon, zeta, all agree as to angular proper motion. delta was toofaint for a spectroscopic measurement, but all the others have beenshown to be approaching us at a rate of twelve to twenty miles asecond. The same has been proved for proper motion, and line of sightmotion, in the case of Pleiades and other groups.

Maskelyne measured many proper motions of stars, from which W.Herschel[8] came to the conclusion that these apparent motions are forthe most part due to a motion of the solar system in space towards apoint in the constellation Hercules, R.A. 257 degrees; N. Decl. 25degrees. This grand discovery has been amply confirmed, and, thoughopinions differ as to the exact direction, it happens that the pointfirst indicated by Herschel, from totally insufficient data, agreeswell with modern estimates.

Comparing the proper motions and parallaxes to get the actual velocityof each star relative to our system, C.L. Struve found the probablevelocity of the solar system in space to be fifteen miles a second, orfive astronomical units a year.

The work of Herschel in this matter has been checked by comparingspectroscopic velocities in the line of sight which, so far as thesun's motion is concerned, would give a maximum rate of approach forstars near Hercules, a maximum rate of recession for stars in theopposite part of the heavens, and no effect for stars half-waybetween. In this way the spectroscope has confirmed generallyHerschel's view of the direction, and makes the velocity eleven milesa second, or nearly four astronomical units a year.

The average proper motion of a first magnitude star has been found tobe 0".25 annually, and of a sixth magnitude star 0".04. But that allbright stars are nearer than all small stars, or that they showgreater proper motion for that reason, is found to be far from thetruth. Many statistical studies have been made in this connection, andinteresting results may be expected from this treatment in the handsof Kapteyn of Groningen, and others.[9]

On analysis of the directions of proper motions of stars in all partsof the heavens, Kapteyn has shown[10] that these indicate, besides thesolar motion towards Hercules, two general drifts of stars in nearlyopposite directions, which can be detected in any part of theheavens. This result has been confirmed from independent data byEddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).

Photography promises to assist in the measurement of parallax andproper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastlyextended the applications of stereoscopic vision to astronomy--asubject which De la Rue took up in the early days of photography. Hehas made a stereo-comparator of great beauty and convenience forcomparing stereoscopically two star photographs taken at differentdates. Wolf of Heidelberg has used this for many purposes. Hisinvestigations depending on the solar motion in space are remarkable.He photographs stars in a direction at right angles to the line of thesun's motion. He has taken photographs of the same region fourteenyears apart, the two positions of his camera being at the two ends ofa base-line over 5,000,000,000 miles apart, or fifty-six astronomicalunits. On examining these stereoscopically, some of the stars rise outof the general plane of the stars, and seem to be much nearer. Many ofthe stars are thus seen to be suspended in space at differentdistances corresponding exactly to their real distances from our solarsystem, except when their proper motion interferes. The effect is moststriking; the accuracy of measurement exceeds that of any other methodof measuring such displacements, and it seems that with a longinterval of time the advantage of the method increases.

_Double Stars._--The large class of double stars has always been muchstudied by amateurs, partly for their beauty and colour, and partly asa test for telescopic definition. Among the many unexplained stellarproblems there is one noticed in double stars that is thought by someto be likely to throw light on stellar evolution. It is this: Thereare many instances where one star of the pair is comparatively faint,and the two stars are contrasted in colour; and in every single casethe general colour of the faint companion is invariably to be classedwith colours more near to the blue end of the spectrum than that ofthe principal star.

_Binary Stars._--Sir William Herschel began his observations of doublestars in the hope of discovering an annual parallax of the stars. Inthis he was following a suggestion of Galileo's. The presumption isthat, if there be no physical connection between the stars of a pair,the largest is the nearest, and has the greatest parallax. So, bynoting the distance between the pair at different times of the year, adelicate test of parallax is provided, unaffected by majorinstrumental errors.

Herschel did, indeed, discover changes of distance, but not of thecharacter to indicate parallax. Following this by further observation,he found that the motions were not uniform nor rectilinear, and by aclear analysis of the movements he established the remarkable andwholly unexpected fact that in all these cases the motion is due to arevolution about their common centre of gravity.[11] He gave theapproximate period of revolution of some of these: Castor, 342 years;delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon Bootis,1,681 years.

Twenty years later Sir John Herschel and Sir James South, afterre-examination of these stars, confirmed[12] and extended the results,one pair of Coronae having in the interval completed more than a wholerevolution.

It is, then, to Sir William Herschel that we owe the extension of thelaw of gravitation, beyond the limits of the solar system, to thewhole universe. His observations were confirmed by F.G.W. Struve (born1793, died 1864), who carried on the work at Dorpat. But it was firstto Savary,[13] and later to Encke and Sir John Herschel, that we owethe computation of the elliptic elements of these stars; also theresulting identification of their law of force with Newton's force ofgravitation applied to the solar system, and the force that makes anapple fall to the ground. As Grant well says in his _History_:"This may be justly asserted to be one of the most sublime truthswhich astronomical science has hitherto disclosed to the researches ofthe human mind."

Latterly the best work on double stars has been done byS. W. Burnham,[14] at the Lick Observatory. The shortest period hefound was eleven years (kappa Pegasi). In the case of some ofthese binaries the parallax has been measured, from which it appearsthat in four of the surest cases the orbits are about the size of theorbit of Uranus, these being probably among the smallest stellarorbits.

The law of gravitation having been proved to extend to the stars, adiscovery (like that of Neptune in its origin, though unlike it in thelabour and originality involved in the calculation) that entrances theimagination became possible, and was realised by Bessel--the discoveryof an unknown body by its gravitational disturbance on one that wasvisible. In 1834 and 1840 he began to suspect a want of uniformity inthe proper motion of Sirius and Procyon respectively. In 1844, in aletter to Sir John Herschel,[15] he attributed these irregularities ineach case to the attraction of an invisible companion, the period ofrevolution of Sirius being about half a century. Later he said: "Iadhere to the conviction that Procyon and Sirius form real binarysystems, consisting of a visible and an invisible star. There is noreason to suppose luminosity an essential quality of cosmicalbodies. The visibility of countless stars is no argument against theinvisibility of countless others." This grand conception led Peters tocompute more accurately the orbit, and to assign the place of theinvisible companion of Sirius. In 1862 Alvan G. Clark was testing anew 18-inch object-glass (now at Chicago) upon Sirius, and, knowingnothing of these predictions, actually found the companion in the veryplace assigned to it. In 1896 the companion of Procyon was discoveredby Professor Schaeberle at the Lick Observatory.

Now, by the refined parallax determinations of Gill at the Cape, weknow that of Sirius to be 0".38. From this it has been calculated thatthe mass of Sirius equals two of our suns, and its intrinsicbrightness equals twenty suns; but the companion, having a mass equalto our sun, has only a five-hundredth part of the sun's brightness.

_Spectroscopic Binaries_.--On measuring the velocity of a star in theline of sight at frequent intervals, periodic variations have beenfound, leading to a belief in motion round an invisiblecompanion. Vogel, in 1889, discovered this in the case of Spica (alphaVirginis), whose period is 4d. 0h. 19m., and the diameter of whoseorbit is six million miles. Great numbers of binaries of this typehave since then been discovered, all of short period.

Also, in 1889, Pickering found that at regular intervals of fifty-twodays the lines in the spectrum of zeta of the Great Bear areduplicated, indicating a relative velocity, equal to one hundred milesa second, of two components revolving round each other, of which thatapparently single star must be composed.

It would be interesting, no doubt, to follow in detail theaccumulating knowledge about the distances, proper motions, and orbitsof the stars; but this must be done elsewhere. Enough has been said toshow how results are accumulating which must in time unfold to us thevarious stellar systems and their mutual relationships.

_Variable Stars._--It has often happened in the history of differentbranches of physical science that observation and experiment were sofar ahead of theory that hopeless confusion appeared to reign; andthen one chance result has given a clue, and from that time alldifferences and difficulties in the previous researches have stoodforth as natural consequences, explaining one another in a rationalsequence. So we find parallax, proper motion, double stars, binarysystems, variable stars, and new stars all bound together.

The logical and necessary explanation given of the cause of ordinaryspectroscopic binaries, and of irregular proper motions of Sirius andProcyon, leads to the inference that if ever the plane of such abinary orbit were edge-on to us there ought to be an eclipse of theluminous partner whenever the non-luminous one is interposed betweenus. This should give rise either to intermittence in the star's lightor else to variability. It was by supposing the existence of a darkcompanion to Algol that its discoverer, Goodricke of York,[16] in1783, explained variable stars of this type. Algol (beta Persei)completes the period of variable brightness in 68.8 hours. It losesthree-fifths of its light, and regains it in twelve hours. In 1889Vogel,[17] with the Potsdam spectrograph, actually found that theluminous star is receding before each eclipse, and approaching usafter each eclipse; thus entirely supporting Goodricke's opinion.There are many variables of the Algol type, and information issteadily accumulating. But all variable stars do not suffer the suddenvariations of Algol. There are many types, and the explanations ofothers have not proved so easy.

The Harvard College photographs have disclosed the very greatprevalence of variability, and this is certainly one of the lines inwhich modern discovery must progress.

Roberts, in South Africa, has done splendid work on the periods ofvariables of the Algol type.

_New Stars_.--Extreme instances of variable stars are the new starssuch as those detected by Hipparchus, Tycho Brahe, and Kepler, ofwhich many have been found in the last half-century. One of the latestgreat "Novae" was discovered in Auriga by a Scotsman, Dr. Anderson, onFebruary 1st, 1892, and, with the modesty of his race, he communicatedthe fact to His Majesty's Astronomer for Scotland on an unsignedpost-card.[18] Its spectrum was observed and photographed by Hugginsand many others. It was full of bright lines of hydrogen, calcium,helium, and others not identified. The astounding fact was that lineswere shown in pairs, bright and dark, on a faint continuous spectrum,indicating apparently that a dark body approaching us at the rate of550 miles a second[19] was traversing a cold nebulous atmosphere, andwas heated to incandescence by friction, like a meteor in ouratmosphere, leaving a luminous train behind it. It almost disappeared,and on April 26th it was of the sixteenth magnitude; but on August17th it brightened to the tenth, showing the principal nebular band inits spectrum, and no sign of approach or recession. It was as if itemerged from one part of the nebula, cooled down, and rushed throughanother part of the nebula, rendering the nebular gas more luminousthan itself.[20]

Since 1892 one Nova after another has shown a spectrum as describedabove, like a meteor rushing towards us and leaving a train behind,for this seems to be the obvious meaning of the spectra.

The same may be said of the brilliant Nova Persei, brighter at itsbest than Capella, and discovered also by Dr. Anderson on February22nd, 1901. It increased in brightness as it reached the densest partof the nebula, then it varied for some weeks by a couple ofmagnitudes, up and down, as if passing through separate nebularcondensations. In February, 1902, it could still be seen with anopera-glass. As with the other Novae, when it first dashed into thenebula it was vaporised and gave a continuous spectrum with dark linesof hydrogen and helium. It showed no bright lines paired with the darkones to indicate a train left behind; but in the end its ownluminosity died out, and the nebular spectrum predominated.

The nebular illumination as seen in photographs, taken from August toNovember, seemed to spread out slowly in a gradually increasing circleat the rate of 90" in forty-eight days. Kapteyn put this down to thevelocity of light, the original outburst sending its illumination tothe nebulous gas and illuminating a spherical shell whose radiusincreased at the velocity of light. This supposition seems correct, inwhich case it can easily be shown from the above figures that thedistance of this Nova was 300 light years.

_Star Catalogues._--Since the days of very accurate observationsnumerous star-catalogues have been produced by individuals or byobservatories. Bradley's monumental work may be said to head the list.Lacaille's, in the Southern hemisphere, was complementary. ThenPiazzi, Lalande, Groombridge, and Bessel were followed by Argelanderwith his 324,000 stars, Rumker's Paramatta catalogue of the southernhemisphere, and the frequent catalogues of national observatories.Later the Astronomische Gesellschaft started their great catalogue,the combined work of many observatories. Other southern ones wereGould's at Cordova and Stone's at the Cape.

After this we have a new departure. Gill at the Cape, having the comet1882.ii. all to himself in those latitudes, wished his friends inEurope to see it, and employed a local photographer to strap hiscamera to the observatory equatoreal, driven by clockwork, andadjusted on the comet by the eye. The result with half-an-hour'sexposure was good, so he tried three hours. The result was such adisplay of sharp star images that he resolved on the Cape PhotographicDurchmusterung, which after fourteen years, with Kapteyn's aid inreducing, was completed. Meanwhile the brothers Henry, of Paris, wereengaged in going over Chacornac's zodiacal stars, and were about tocatalogue the Milky Way portion, a serious labour, when they sawGill's Comet photograph and conceived the idea of doing the rest oftheir work by photography. Gill had previously written to AdmiralMouchez, of the Paris Observatory, and explained to him his projectfor charting the heavens photographically, by combining the work ofmany observatories. This led Admiral Mouchez to support the brothersHenry in their scheme.[21] Gill, having got his own photographic workunderway, suggested an international astrographic chart, the materialsfor different zones to be supplied by observatories of all nations,each equipped with similar photographic telescopes. At a conference inParis, 1887, this was decided on, the stars on the charts going downto the fourteenth magnitude, and the catalogues to the eleventh.

This monumental work is nearing completion. The labour involved wasimmense, and the highest skill was required for devising instrumentsand methods to read off the star positions from the plates.

Then we have the Harvard College collection of photographic plates,always being automatically added to; and their annex at Arequipa inPeru.

Such catalogues vary in their degree of accuracy; and fundamentalcatalogues of standard stars have been compiled. These requireextension, because the differential methods of the heliometer and thecamera cannot otherwise be made absolute.

The number of stars down to the fourteenth magnitude may be taken atabout 30,000,000; and that of all the stars visible in the greatestmodern telescopes is probably about 100,000,000.

_Nebulae and Star-clusters._--Our knowledge of nebulae really dates fromthe time of W. Herschel. In his great sweeps of the heavens with hisgiant telescopes he opened in this direction a new branch ofastronomy. At one time he held that all nebulae might be clusters ofinnumerable minute stars at a great distance. Then he recognised thedifferent classes of nebulae, and became convinced that there is awidely-diffused "shining fluid" in space, though many so-called nebulaecould be resolved by large telescopes into stars. He considered thatthe Milky Way is a great star cluster, whose form may be conjecturedfrom numerous star-gaugings. He supposed that the compact "planetarynebulae" might show a stage of evolution from the diffuse nebulae, andthat his classifications actually indicate various stages ofdevelopment. Such speculations, like those of the ancients about thesolar system, are apt to be harmful to true progress of knowledgeunless in the hands of the ablest mathematical physicists; andHerschel violated their principles in other directions. But here hisspeculations have attracted a great deal of attention, and, withmodifications, are accepted, at least as a working hypothesis, by afair number of people.

When Sir John Herschel had extended his father's researches into theSouthern Hemisphere he was also led to the belief that some nebulaewere a phosphorescent material spread through space like fog or mist.

Then his views were changed by the revelations due to the greatdiscoveries of Lord Rosse with his gigantic refractor,[22] when onenebula after another was resolved into a cluster of minute stars. Atthat time the opinion gained ground that with increase of telescopicpower this would prove to be the case with all nebulae.

In 1864 all doubt was dispelled by Huggins[23] in his first examinationof the spectrum of a nebula, and the subsequent extension of thisobservation to other nebulae; thus providing a certain test whichincrease in the size of telescopes could never have given. In 1864Huggins found that all true nebulae give a spectrum of brightlines. Three are due to hydrogen; two (discovered by Copeland) arehelium lines; others are unknown. Fifty-five lines have beenphotographed in the spectrum of the Orion nebula. It seems to bepretty certain that all true nebulae are gaseous, and show almostexactly the same spectrum.

Other nebulae, and especially the white ones like that in Andromeda,which have not yet been resolved into stars, show a continuousspectrum; others are greenish and give no lines.

A great deal has to be done by the chemist before the astronomer canbe on sure ground in drawing conclusions from certain portions of hisspectroscopic evidence.

The light of the nebulas is remarkably actinic, so that photographyhas a specially fine field in revealing details imperceptible in thetelescope. In 1885 the brothers Henry photographed, round the starMaia in the Pleiades, a spiral nebula 3' long, as bright on the plateas that star itself, but quite invisible in the telescope; and anexposure of four hours revealed other new nebula in the samedistrict. That painstaking and most careful observer, Barnard, with10-1/4 hours' exposure, extended this nebulosity for several degrees,and discovered to the north of the Pleiades a huge diffuse nebulosity,in a region almost destitute of stars. By establishing a 10-inchinstrument at an altitude of 6,000 feet, Barnard has revealed the widedistribution of nebular matter in the constellation Scorpio over aspace of 4 degrees or 5 degrees square. Barnard asserts that the "nebularhypothesis" would have been killed at its birth by a knowledge ofthese photographs. Later he has used still more powerful instruments,and extended his discoveries.

The association of stars with planetary nebulae, and the distributionof nebulae in the heavens, especially in relation to the Milky Way, arestriking facts, which will certainly bear fruit when the time arrivesfor discarding vague speculations, and learning to read the truephysical structure and history of the starry universe.

_Stellar Spectra._--When the spectroscope was first available forstellar research, the leaders in this branch of astronomy were Hugginsand Father Secchi,[24] of Rome. The former began by devoting years ofwork principally to the most accurate study of a few stars. Thelatter devoted the years from 1863 to 1867 to a general survey of thewhole heavens, including 4,000 stars. He divided these into fourprincipal classes, which have been of the greatest service. Half ofhis stars belonged to the first class, including Sirius, Vega,Regulus, Altair. The characteristic feature of their spectra is thestrength and breadth of the hydrogen lines and the extreme faintnessof the metallic lines. This class of star is white to the eye, andrich in ultra violet light.

The second class includes about three-eighths of his stars, includingCapella, Pollux, and Arcturus. These stars give a spectrum like thatof our sun, and appear yellowish to the eye.

The third class includes alpha Herculis, alpha Orionis (Betelgeux), MiraCeti, and about 500 red and variable stars. The spectrum has flutedbands shaded from blue to red, and sharply defined at the morerefrangible edge.

The fourth class is a small one, containing no stars over fifthmagnitude, of which 152 Schjellerup, in Canes Venatici, is a goodexample. This spectrum also has bands, but these are shaded on theviolet side and sharp on the red side. They are due to carbon in someform. These stars are ruby red in the telescope.

It would appear, then, that all stars are suns with continuousspectra, and the classes are differentiated by the character of theabsorbent vapours of their atmospheres.

It is very likely that, after the chemists have taught us how tointerpret all the varieties of spectrum, it will be possible toascribe the different spectrum-classes to different stages in thelife-history of every star. Already there are plenty of people readyto lay down arbitrary assumptions about the lessons to be drawn fromstellar spectra. Some say that they know with certainty that each starbegins by being a nebula, and is condensed and heated by condensationuntil it begins to shine as a star; that it attains a climax oftemperature, then cools down, and eventually becomes extinct. They goso far as to declare that they know what class of spectrum belongs toeach stage of a star's life, and how to distinguish between one thatis increasing and another that is decreasing in temperature.

The more cautious astronomers believe that chemistry is notsufficiently advanced to justify all of these deductions; that, untilchemists have settled the lately raised question of the transmutationof elements, no theory can be sure. It is also held that until theyhave explained, without room for doubt, the reasons for the presenceof some lines, and the absence of others, of any element in a stellarspectrum; why the arc-spectrum of each element differs from its sparkspectrum; what are all the various changes produced in the spectrum ofa gas by all possible concomitant variations of pressure andtemperature; also the meanings of all the flutings in the spectra ofmetalloids and compounds; and other equally pertinent matters--untilthat time arrives the part to be played by the astronomer is one ofobservation. By all means, they say, make use of "working hypotheses"to add an interest to years of laborious research, and to serve as aguide to the direction of further labours; but be sure not to fallinto the error of calling any mere hypothesis a theory.

_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as itwere, tentatively put forward by Laplace as a note in his _Systeme duMonde_, supposes the solar system to have been a flat, disk-shapednebula at a high temperature in rapid rotation. In cooling itcondensed, leaving revolving rings at different distances from thecentre. These themselves were supposed to condense into the nucleusfor a rotating planet, which might, in contracting, again throw offrings to form satellites. The speculation can be put in a reallyattractive form, but is in direct opposition to many of the actualfacts; and so long as it is not favoured by those who wish to maintainthe position of astronomy as the most exact of the sciences--exact inits facts, exact in its logic--this speculation must be recorded bythe historian, only as he records the guesses of the ancient Greeks--asan interesting phase in the history of human thought.

Other hypotheses, having the same end in view, are the meteoritichypothesis of Lockyer and the planetesimal hypothesis that has beenlargely developed in the United States. These can best be read in theoriginal papers to various journals, references to which may be foundin the footnotes of Miss Clerke's _History of Astronomy during theNineteenth Century_. The same can be said of Bredichin's hypothesis ofcomets' tails, Arrhenius's book on the applications of the theory oflight repulsion, the speculations on radium, the origin of the sun'sheat and the age of the earth, the electron hypothesis of terrestrialmagnetism, and a host of similar speculations, all combining to throwan interesting light on the evolution of a modern train of thoughtthat seems to delight in conjecture, while rebelling against thatstrict mathematical logic which has crowned astronomy as the queen ofthe sciences.

FOOTNOTES:

[1] _R. S. Phil Trans_., 1810 and 1817-24.

[2] One of the most valuable contributions to our knowledge of stellarparallaxes is the result of Gill's work (_Cape Results_, vol. iii.,part ii., 1900).

[3] Taking the velocity of light at 186,000 miles a second, and theearth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000miles or 63,072 astronomical units; 1 astronomical unit a year=2.94miles a second; and the earth's orbital velocity=18.5 miles a second.

[4] Ast. Nacht., 1889.

[5] R. S. Phil. Trans., 1718.

[6] Mem. Acad. des Sciences, 1738, p. 337.

[7] R. S Phil. Trans., 1868.

[8] _R.S. Phil Trans._, 1783.

[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill'spresidential address to the British Association, 1907.

[20] For a different explanation see Sir W. Huggins's lecture, RoyalInstitution, May 13th, 1892.

[21] For the early history of the proposals for photographiccataloguing of stars, see the _Cape Photographic Durchmusterung_, 3vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,Introduction.)